I came across some threads where I found this text on the top.
Warning: One or more bitcointalk.org users have reported that they believe that the creator of this topic displays some red flags which make them high-risk. (Check their trust page to see the detailed trust ratings.) While the bitcointalk.org administration does not verify such claims, you should proceed with extreme caution.
These warning banners will disappear when you have 7 days of login time. You should familiarize yourself with the trust system before then.

my query has two parts
1. If someone gives you a negative trust, can you fight back like proving yourself correct and removing the negative trust from your profile.
2. what advantage you get if you give someone a negative trust?
If you give some a negative feedback be sure it is reasonable or you will be reported as abusing it and worse scenario is if you are giving a bad feedback to a DT1 you will harm yourself more than you harm the one that you give feedback, don't fight back feedback if he cannot prove the allegation and if he is not part of the DT group.